Connecting Math and Science in the World
The bicycle, which many kids are still familiar with, provides an opportunity to investigate some real-world science that is tangible in many kids lives. The gears are the most obvious, but there is also opportunity to talk about friction (brakes), rolling resistance (tires), lubrication (chain, wheels, bottom bracket), and momentum of a spinning wheel.
Gears
On many of the bicycles we ride, there are a collection of cogs on the back wheel and one, two or three chain rings at the pedals as this video illustrates. Many people don't understand them, don't use them properly and don't benefit from their existence on their bike. How often have you seen someone walking their bike up the hill because they found it too difficult to pedal? The reality is that they just didn't put their bike in the right gear or their bike didn't have a low enough gear or their bike wouldn't shift into the lowest gear because of a maintenance problem. Most bikes that regular people buy have a low enough gear for them to climb most hills more easily than if they walk up the hill.
What this table is showing is the ratio of the number of teeth on the front chain ring to the number of teeth on the cog on the back chain ring. Looking at the first item in the table 2.00, this is the number of times the back wheel will go around if the chain is on the 22 tooth chain ring and the 11 tooth rear cog. Similarly when the chain is on the 32 tooth chain ring and the 16 tooth cog at the back, the wheel will go around two times for each one turn of the pedals.
The combination of three front chair rings that many mountain bikes have and the cluster of 7-11 cogs at the back wheel make shifting seem even more complicated. As the table illustrates, there are several chain ring/cog combinations in the table that create the same gear ratio. For example, each chain ring can create a 2.0 ratio which means the rider feels the same resistance when pedaling. This introduces a discussion of the best shifting pattern to use to get the most linear progression of gears with the least shifting and the best bike performance.
Friction
Squeezing the brakes on the spinning wheel of a bicycle will usually bring the bike to a stop if the brakes are working properly. Bike brakes provide an easy method to start to understand friction and its effect and what happens when the brake pads get wet. We can also talk about the law of conservation of energy at a high level by discussing why the brake pads get warm when there's a lot of braking. Friction can also be talked about in the shifting and brake cables.
Rolling Resistance
Different tires can have a really big effect on the rolling resistance of a bike wheel. This can lead to an opportunity to talk about: narrow tires that are inflated to high pressure, wider tires at lower pressure, knobby tires, and other wheels like steel train wheels.
Lubrication
Lubrication is important in many places on a bike including the wheel hubs, the bottom bracket, the chain and the shifting cables.
Momentum of a spinning wheel
The operation of a gyroscope is fascinating and can be replicated with a spinning bicycle wheel. Demonstrating the gyroscopic action with a wheel helps students to understand why a bicycle doesn't fall over easily when it's moving.
Supporting Resources
www.abc.net.au/science/surfingscientist/pdf/teachdemo15.pdf
http://www.howstuffworks.com/gyroscope.htm